There are a couple of limitations for these approaches.
First, a Bayes factor that includes a model with small posterior probability
will suffer from Monte Carlo error.
For example, unless a very large sample from the posterior is collected, some
models might not be sampled at all.
A potential solution to this problem is adjusting the prior probabilities of
the models such that none of their posterior probabilities are very small
[1]}, [2]}.
Second, and perhaps more importantly, for these numerical algorithms to be able
to “jump” among models, the models being sampled need to be similar.
Whereas the first limitation is specific to using model averaging to estimate
Bayes factors, the second problem is more general.
